We have the function f(x) = (3/2) x – 9/2 and we have to find the inverse function.

Let y = f(x) = (3/2) x – 9/2

=> y = (3/2) x – 9/2

=> 2y = 3x - 9

=> 2y + 9 = 3x

=> x = 2y/3 + 9/3

=> x = 2y/3 + 3

interchange x and y

=> y = 2x/3 + 3

**Therefore the inverse of f(x) or f^-1(x) = 2x/3 + 3.**

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